To document a function, it is often helpful to have an example script which uses your function. The publish function in Matlab can then be used to generate a help file with embedded pictures, code, links, etc. The syntax for documenting your code can be found here.
The Function This function uses a "corrected" FFT in Matlab.
function out_sig = myfft(in_sig) out_sig = fftshift(fft(ifftshift(in_sig))); end
The Example Script This is a separate script which explains the inputs, outputs, and gives an example explaining why the correction is necessary. Thanks to Wu, Kan, the original author of this function.
%% myfft % This function uses the "proper" fft in matlab. Note that the fft needs to % be multiplied by dt to have physical significance. % For a full description of why the FFT should be taken like this, refer % to: Why_use_fftshift(fft(fftshift(x)))__in_Matlab.pdf included in the % help folder of this code. Additional information can be found: % <https://www.mathworks.com/matlabcentral/fileexchange/25473-why-use-fftshift-fft-fftshift-x----in-matlab-instead-of-fft-x--> % %% Inputs % *in_sig* - 1D signal % %% Outputs % *out_sig* - corrected FFT of *in_sig* % %% Examples % Generate a signal with an analytical solution. The analytical solution is % then compared to the fft then to myfft. This example is a modified % version given by Wu, Kan given in the link aboce. %% % Set parameters fs = 500; %sampling frequency dt = 1/fs; %time step T=1; %total time window t = -T/2:dt:T/2-dt; %time grids df = 1/T; %freq step Fmax = 1/2/dt; %freq window f=-Fmax:df:Fmax-df; %freq grids, not used in our examples, could be used by plot(f, X) %% % Generate Gaussian curve Bx = 10; A = sqrt(log(2))/(2*pi*Bx); %Characteristics of Gaussian curve x = exp(-t.^2/2/A^2); %Create Gaussian Curve %% % Generate Analytical solution Xan = A*sqrt(2*pi)*exp(-2*pi^2*f.^2*A^2); %X(f), real part of the analytical Fourier transform of x(t) %% % Take FFT and corrected FFT then compare Xfft = dt *fftshift(fft(x)); %FFT Xfinal = dt * myfft(x); %Corrected FFT hold on plot(f,Xan); plot(f,real(Xfft)); plot(f,real(Xfinal),'ro'); title('Comparison of Corrected and Uncorrected FFT'); legend('Analytical Solution','Uncorrected FFT','Corrected FFT'); xlabel('Frequency'); ylabel('Amplitude'); DT = max(f) - min(f); xlim([-DT/4,DT/4]);
The Output The publish option can be found under the "Publish" tab, highlighted in the imageSimple Function Documentation below.
Matlab will run the script, and save the images which are displayed, as well as the text generated by the command line. The output can be saved to many different types of formats, including HTML, Latex, and PDF.
The output of the example script given above can be seen in the image below.